대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제21권3호
  • /
  • Pages.429-432
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  • 2006
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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A NEW NON-MEASURABLE SET AS A VECTOR SPACE

  • Chung, Soon-Yeong (Department of Mathematics and the Program of Integrated Biotechnology Sogang University)
  • 발행 : 2006.07.01
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초록

We use Cauchy's functional equation to construct a new non-measurable set which is a (vector) subspace of \mathbb{R}$ and is of a codimensiion 1, considering \mathbb{R}$, the set of real numbers, as a vector space over a field \mathbb{Q}$ of rational numbers. Moreover, we show that \mathbb{R}$ can be partitioned into a countable family of disjoint non-measurable subsets.

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참고문헌

  1. G. de Barra, Measure Theory and Integration, Ellis Horwod Limited, New York, 1981
  2. G. H. Hardy, J. E. Littlewood, and G. Polya, Inequalities, Cambridge University Press, New York, 1952